degree:12
 order:54
[ 12, 12, 1, 12, 16 ][ 1, 0, 2, 3, 12, 2, 3, 0, 0, 3 ]

minimal polynomial:[ x-12, x-3, x, x+3, x^2-3*x-12 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^6-9*x^5-57*x^4+225*x^3+432*x^2-1296*x
x^2-1
x^4-12*x^3-36*x^2+432*x
x^5-10*x^4-120*x^3+320*x^2+1024*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 4, 1, 0, 2, 4 ], [ 0, 1, 4, 1, 2, 4 ], 
      [ 0, 0, 12, 0, 0, 0 ], [ 0, 2, 2, 0, 4, 4 ], [ 0, 3, 3, 0, 3, 3 ] ], 
  [ [ 0, 0, 12, 0, 0, 0 ], [ 0, 1, 4, 1, 2, 4 ], [ 1, 4, 1, 0, 2, 4 ], 
      [ 0, 12, 0, 0, 0, 0 ], [ 0, 2, 2, 0, 4, 4 ], [ 0, 3, 3, 0, 3, 3 ] ], 
  [ [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], 
      [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 0, 12, 0 ], [ 0, 2, 2, 0, 4, 4 ], [ 0, 2, 2, 0, 4, 4 ], 
      [ 0, 0, 0, 0, 12, 0 ], [ 1, 4, 4, 1, 2, 0 ], [ 0, 3, 3, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 0, 16 ], [ 0, 4, 4, 0, 4, 4 ], [ 0, 4, 4, 0, 4, 4 ], 
      [ 0, 0, 0, 0, 0, 16 ], [ 0, 4, 4, 0, 0, 8 ], [ 1, 3, 3, 1, 6, 2 ] ] ]